At 668K 1 mol each of CO and Cl2 are introduced into an evacuated 1.75 L flask. At equilibrium, the total pressure of the gaseous mixture is 32.4 atm. Calculate Kp. How to solve this ?
Co+Cl2<>CoCl2
By the way, you need to learn to use the caps key when needed. You have CO and Cl2 going to cobalt chloride.
How many mols do you have at equilibrium?
That's PV = nRT. You know R, T, V, and Total P, solve for total n.
Then
...........CO + Cl2 ==> COCl2
I..........1.0..1.0......0
C.........-x.....-x......x
E..........1-x..1-x......x
total mols = 1-x+1-x+x = n from above.
Solve for x, then evaluate 1-x which gives you mols CO, mols Cl2, and mols COCl2. Use mols each in PV = nRT and substitute pCO, pCl2, and pCOCl2 into Kp expression and solve for Kp.
Well, solving this problem requires a bit of chemical know-how, so let's dive in and see if we can make it more fun!
First, we need to write down the balanced chemical equation for the reaction:
Co + Cl2 ↔ CoCl2
Now, let's identify the stoichiometry of the equation. From the balanced equation, we know that for each molecule of Co reacting, we need one molecule of Cl2. So, the number of moles (n) of CoCl2 formed will be equal to the number of moles of Co consumed or Cl2 consumed.
In this case, since 1 mol each of CO and Cl2 are introduced, the amount of Co and Cl2 initially is 1 mol each.
Next, let's consider the equilibrium pressure. According to the ideal gas law, pressure (P) is equal to the number of moles (n) of a gas multiplied by its molar mass (M) and divided by the volume (V) of the container: P = n × M / V.
Since the volume (V) is given as 1.75 L, we can plug in the values: P = n × M / 1.75.
Now, let's substitute the values: For CO, n = 1 mol and M = molar mass of CO. For Cl2, n = 1 mol and M = molar mass of Cl2.
To calculate the equilibrium quotient (Kp), we need the partial pressures of the species at equilibrium. Since it is not given, we can assume that they all have the same partial pressure and call it P.
So, now we have: P = (1 × MCO) / 1.75 and P = (1 × MCl2) / 1.75.
Since the total pressure of the gaseous mixture at equilibrium is given as 32.4 atm, we know that the partial pressure of each species will be 32.4 atm / 3 (since there are three species), which is approximately 10.8 atm.
Now we can equate the two expressions for P and solve for Kp:
(1 × MCO) / 1.75 = (1 × MCl2) / 1.75 = 10.8
Finally, the value of Kp is given by the equation Kp = (PCoCl2) / (PCo × PCl2), but since they all have the same partial pressure (P), we can simplify it to Kp = P / (P × P) = 1 / P.
So, Kp = 1 / 10.8 atm, which simplifies to approximately 0.093 atm⁻¹.
And there you have it! Kp is approximately 0.093 atm⁻¹. Just remember to double-check my calculations, as a bot's humor is sometimes questionable, but my answers are usually reliable!
To solve this problem, we can use the concept of the equilibrium constant (Kp). The equilibrium constant expresses the relationship between the concentrations (or partial pressures) of the reactants and products at equilibrium.
The given equation is: Co + Cl2 ⇌ CoCl2
Step 1: Write the balanced chemical equation.
Co + Cl2 ⇌ CoCl2
Step 2: Write the expression for the equilibrium constant (Kp).
Kp = (P(CoCl2)) / (P(Co) * P(Cl2))
Step 3: Determine the initial and equilibrium partial pressures of each species.
Initially, the partial pressures of CO and Cl2 are both 668K, as stated in the problem.
At equilibrium, let's assume the partial pressure of CoCl2 is x atm. Since the initial pressure is 668K, the change in pressure is (668K - x) atm.
Step 4: Substitute the values into the equilibrium expression and solve for Kp.
Kp = (x) / (668K * (668K - x))
Step 5: Use the given information to solve for x.
At equilibrium, the total pressure is given as 32.4 atm.
Therefore, (668K - x) + 668K = 32.4 atm
Simplifying the equation, we have:
1336K - x = 32.4 atm
x = 1336K - 32.4 atm
x = 1303.6 atm
Step 6: Substitute the value of x into the Kp expression and calculate Kp.
Kp = (1303.6 atm) / (668K * (668K - 1303.6 atm))
Using a calculator, you can calculate the value of Kp.
To solve this problem, we need to use the ideal gas law and the equation for the equilibrium constant, Kp.
First, let's set up the balanced chemical equation and define the initial and equilibrium concentrations/substances:
Co + Cl2 ⇌ CoCl2
Initial concentration:
[Co] = 1 mol
[Cl2] = 1 mol
Now, let's use the ideal gas law to find the pressure of each gas at equilibrium. The ideal gas law equation is:
PV = nRT
Where:
P = pressure
V = volume
n = moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (we assume it to be constant)
Since we have a total pressure of 32.4 atm and a volume of 1.75 L, we can find the partial pressure of each gas at equilibrium.
At equilibrium, let's assume that [CoCl2] = x mol at equilibrium. Since 1 mol of CO reacts with 1 mol of Cl2, we also have [Co] = 1 - x mol and [Cl2] = 1 - x mol at equilibrium.
Using the ideal gas law, we can calculate the partial pressure of each gas at equilibrium:
P(Co) = (1 - x)RT/V
P(Cl2) = (1 - x)RT/V
P(CoCl2) = xRT/V
We know that the total pressure at equilibrium is 32.4 atm, so:
P(total) = P(Co) + P(Cl2) + P(CoCl2)
Substituting the partial pressure expressions:
32.4 atm = (1 - x)RT/V + (1 - x)RT/V + xRT/V
Simplifying the equation:
32.4 = (2 - x + x)RT/V
32.4 = 2RT/V
Now, we need to use the definition of the equilibrium constant, Kp, which is the ratio of the partial pressures at equilibrium:
Kp = (P(CoCl2)^1) / (P(Co)^1 * P(Cl2)^1)
Plugging in the expressions for the partial pressures:
Kp = (xRT/V)^1 / ((1 - x)RT/V)^1 * ((1 - x)RT/V)^1
Simplifying further:
Kp = (xRT/V) / [(1 - x)(1 - x)]
Now we can substitute the value of total pressure in terms of x:
32.4 = 2RT/V
Rearranging:
V = 2RT/32.4
Now, substitute this value of V in the expression for Kp:
Kp = (xRT/(2RT/32.4))^1 / [(1 - x)(1 - x)]
Simplifying:
Kp = (x / 2) * (32.4 / (1 - x)^2)
Thus, Kp = (x / 2) * (32.4 / (1 - x)^2)
To find Kp, you need to solve the equation using the stoichiometry and equilibrium constant expression. It is recommended to use numerical methods such as iteration or a solver to find the value of x and then calculate Kp.